Non sequitur (logic)

A non sequitur (Latin for "it does not follow"), in formal logic, is an invalid argument – an argument whose conclusion does not follow from its premises.[1] In a non sequitur, the conclusion could be either true or false (because there is a disconnect between the premises and the conclusion), but the argument nonetheless asserts the conclusion to be true and is thus fallacious. While a logical argument is a non sequitur if, and only if, it is invalid (and so, technically, the terms 'invalid argument' and 'non sequitur' are equivalent), the word 'non sequitur' is typically used to refer to those types of invalid arguments which do not constitute logical fallacies covered by particular terms (e.g. affirming the consequent). In other words, in practice, 'non sequitur' is used to refer to an unnamed logical fallacy. Often, in fact, 'non sequitur' is used when an irrelevancy is showing up in the conclusion. The term has special applicability in law, having a formal legal definition.[further explanation needed]

While B can indeed be false, this cannot be linked to the premise since the statement is a non sequitur. This is called denying the antecedent.

An example of denying the antecedent would be:

If I am Japanese, then I am Asian.

I am not Japanese.

Therefore, I am not Asian.

While the conclusion may be true, it does not follow from the premise. For all the reader knows, the declarant of the statement could be Asian, but for example Chinese, in which case the premise would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

The conclusion does not follow from the premise as it could be the case that A and B are both true. This fallacy stems from the stated definition of or in propositional logic to be inclusive.

An example of affirming a disjunct would be:

I am at home or I am in the city.

I am at home.

Therefore, I am not in the city.

While the conclusion may be true, it does not follow from the premise. For all the reader knows, the declarant of the statement very well could be in both the city and their home, in which case the premises would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

*Note that this is only a logical fallacy when the word "or" is in its inclusive form. If the two possibilities in question are mutually exclusive, this is not a logical fallacy. For example,

The conclusion does not follow from the premise as it could be the case that A and B are both false.

An example of denying a conjunct would be:

I cannot be both at home and in the city.

I am not at home.

Therefore, I am in the city.

While the conclusion may be true, it does not follow from the premise. For all the reader knows, the declarant of the statement very well could neither be at home nor in the city, in which case the premise would be true but the conclusion false. This argument is still a fallacy even if the conclusion is true.

It may or may not be the case that "all Zs are Bs", but in either case it is irrelevant to the conclusion. What is relevant to the conclusion is whether it is true that "all Bs are Zs," which is ignored in the argument.

An example can be given as follows, where B=mammals, Y=Mary and Z=humans:

All humans are mammals.

Mary is a mammal.

Therefore, Mary is a human.

Note that if the terms (Z and B) were swapped around in the first co-premise then it would no longer be a fallacy and would be correct.